Re: [R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi Chris, OK - stick with the RAM model, the h2 is so high you will run into numerical issues otherwise. In the two-trait model you might want to add in us(at.level(trait,1)):units into the random effects (make sure it is not the last term in the random formula) in case log.dep has a h2 substantially less than 1. Having a multi-level response will help with power so I would go for it. threshBayes does handle ordinal responses but you would probably have to run it for a VERY long time to sample the posterior adequately. Cheers, Jarrod On 16/12/2016 07:11, Chris Mull wrote: Hi Jarrod, I hadn't appreciated that the clustering of reproductive modes on the tree might limit out ability to detect some of these relationships. This is in fact a step in testing reproduction as an ordinal variable (egg-laying, lecithotrophic live-bearing, and matrotrophic live-bearing) which follows gradients of depth and latitude, and threshBayes cannot handle ordinal variables. Perhaps treating the data this way will help given more transitions. I have run the model in MCMCglmm and have appended the summary and attached the histogram of the liabilities. Thanks so much for your help with this... summary(dep2) Iterations = 3001:12991 Thinning interval = 10 Sample size = 1000 DIC: 31.2585 G-structure: ~animal post.mean l-95% CI u-95% CI eff.samp animal 82.1835.88140.16.266 R-structure: ~units post.mean l-95% CI u-95% CI eff.samp units 1110 Location effects: parity ~ log.med.depth post.mean l-95% CI u-95% CI eff.samp pMCMC (Intercept) 0.4250 -13.5697 13.791328.54 0.946 log.med.depth -0.3601 -4.4399 3.802216.48 0.862 On Thu, Dec 15, 2016 at 11:10 PM, Jarrod Hadfield> wrote: Hi Chris, I think MCMCglmm is probably giving you the right answer. There are huge chunks of the phylogeny that are either egg-laying and live-bearing. The non-phylogenetic model shows a strong relationship between reproductive mode and depth, and that might be causal or it might just be because certain taxa tend to live at greater depths and *happen to have* the same reproductive mode. There's not much information in the phylogenetic spread of reproductive modes to distinguish between these hypotheses, hence the wide confidence intervals. Just to be sure can you a) just perform independent contrasts (not really suitable for binary data, but probably won't give you an answer far off the truth and is a nice simple sanity check). b) using MCMCglmm (not MCMCglmmRAM) fit prior.dep2<-=list(R=list(V=diag(1), fix=1), G=list(G1=list(V=diag(1), nu=0.002))) dep2<-MCMCglmm(parity~log.med.depth, random=~animal, rcov=~units, pedigree=shark.tree, data=traits, prior=prior.dep2, pr=TRUE, pl=TRUE, family="threshold") an send me the summary and hist(dep2$Liab) Cheers, Jarrod On 16/12/2016 07:02, Jarrod Hadfield wrote: Hi Chris, I think ngen in threshbayes is not the number of full iterations (i.e. a full update of all parameters), but the number of full iterations multiplied by the number of nodes (2n-1). With n=600 species this means threshbayes has only really done about 8,000 iterations (i.e. about 1000X less than MCMCglmm). Simulations suggest threshbayes is about half as efficient per full iteration as MCMCglmm which means that it may have only collected 0.5*1132/1200 = 0.47 effective samples from the posterior. The very extreme value and the surprisingly tight credible intervals (+/-0.007) also suggest a problem. **However**, the low effective sample size for the covariance in the MCMglmm model is also worrying given the length of chain, and may point to potential problems. Are egg-laying/live-bearing scattered throughout the tree, or do they tend to aggregate a lot? Can you send me the output from: prior.dep<-=list(R=list(V=diag(1)*1e-15, fix=1), G=list(G1=list(V=diag(1), fix=1))) dep<-MCMCglmm(parity~log.med.depth, random=~animal, rcov=~units, pedigree=shark.tree, reduced=TRUE, data=traits, prior=prior2, pr=TRUE, pl=TRUE, family="threshold") summary(dep) summary(glm(parity~log.med.depth, data=traits, family=binomial(link=probit))) Cheers, Jarrod On 15/12/2016 20:59, Chris Mull wrote: Hi All, I am trying to look at the
Re: [R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi Jarrod, I hadn't appreciated that the clustering of reproductive modes on the tree might limit out ability to detect some of these relationships. This is in fact a step in testing reproduction as an ordinal variable (egg-laying, lecithotrophic live-bearing, and matrotrophic live-bearing) which follows gradients of depth and latitude, and threshBayes cannot handle ordinal variables. Perhaps treating the data this way will help given more transitions. I have run the model in MCMCglmm and have appended the summary and attached the histogram of the liabilities. Thanks so much for your help with this... summary(dep2) Iterations = 3001:12991 Thinning interval = 10 Sample size = 1000 DIC: 31.2585 G-structure: ~animal post.mean l-95% CI u-95% CI eff.samp animal 82.1835.88140.16.266 R-structure: ~units post.mean l-95% CI u-95% CI eff.samp units 1110 Location effects: parity ~ log.med.depth post.mean l-95% CI u-95% CI eff.samp pMCMC (Intercept) 0.4250 -13.5697 13.791328.54 0.946 log.med.depth -0.3601 -4.4399 3.802216.48 0.862 On Thu, Dec 15, 2016 at 11:10 PM, Jarrod Hadfieldwrote: > Hi Chris, > > I think MCMCglmm is probably giving you the right answer. There are huge > chunks of the phylogeny that are either egg-laying and live-bearing. The > non-phylogenetic model shows a strong relationship between reproductive > mode and depth, and that might be causal or it might just be because > certain taxa tend to live at greater depths and *happen to have* the same > reproductive mode. There's not much information in the phylogenetic spread > of reproductive modes to distinguish between these hypotheses, hence the > wide confidence intervals. Just to be sure can you > > a) just perform independent contrasts (not really suitable for binary > data, but probably won't give you an answer far off the truth and is a nice > simple sanity check). > > b) using MCMCglmm (not MCMCglmmRAM) fit > > prior.dep2<-=list(R=list(V=diag(1), fix=1), G=list(G1=list(V=diag(1), > nu=0.002))) > > dep2<-MCMCglmm(parity~log.med.depth, >random=~animal, >rcov=~units, >pedigree=shark.tree, >data=traits, >prior=prior.dep2, >pr=TRUE, >pl=TRUE, >family="threshold") > > an send me the summary and hist(dep2$Liab) > > Cheers, > > Jarrod > > > > On 16/12/2016 07:02, Jarrod Hadfield wrote: > > Hi Chris, > > I think ngen in threshbayes is not the number of full iterations (i.e. a > full update of all parameters), but the number of full iterations > multiplied by the number of nodes (2n-1). With n=600 species this means > threshbayes has only really done about 8,000 iterations (i.e. about 1000X > less than MCMCglmm). Simulations suggest threshbayes is about half as > efficient per full iteration as MCMCglmm which means that it may have only > collected 0.5*1132/1200 = 0.47 effective samples from the posterior. The > very extreme value and the surprisingly tight credible intervals (+/-0.007) > also suggest a problem. > > **However**, the low effective sample size for the covariance in the > MCMglmm model is also worrying given the length of chain, and may point to > potential problems. Are egg-laying/live-bearing scattered throughout the > tree, or do they tend to aggregate a lot? Can you send me the output from: > > prior.dep<-=list(R=list(V=diag(1)*1e-15, fix=1), > G=list(G1=list(V=diag(1), fix=1))) > > dep<-MCMCglmm(parity~log.med.depth, >random=~animal, >rcov=~units, >pedigree=shark.tree, >reduced=TRUE, >data=traits, >prior=prior2, >pr=TRUE, >pl=TRUE, >family="threshold") > > summary(dep) > > summary(glm(parity~log.med.depth, data=traits, > family=binomial(link=probit))) > > Cheers, > > Jarrod > > > > On 15/12/2016 20:59, Chris Mull wrote: > > Hi All, > I am trying to look at the correlated evolution of traits using the > threshold model as implemented in phytools::threshBayes (Revell 2014) and > MCMCglmmRAM (Hadfield 2015). My understanding from Hadfield 2015 is that > the reduced animal models should yeild equivalent results, yet having run > both I am having trouble reconciling the results. I have a tree covering > ~600 species of sharks. skates, and rays and am interested in testing for > the correlated evolution between reproductive mode (egg-laying and > live-bearing) with depth. When I test for this correlation using > phytools:threshBayes there is a clear result with a high correlation > coefficient (-0.986) as I would predict. When I run the same analysis using > MCMCglmmRAM I get a very different result, with
Re: [R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi Jarrod, Thanks very much for your fast reply. Egg-laying and live-bearing are dispersed throughout the tree ( I have attached a PDF of a traitplot with egg-laying and live-bearing on it; blue is egg-laying and red is live-bearing), being universal in chimaeras and skates, and found in several families of galeomorph sharks. Here are the summaries of the two models: # >summary(dep) Iterations = 3001:12991 Thinning interval = 10 Sample size = 1000 DIC: 62.7561 G-structure: ~animal post.mean l-95% CI u-95% CI eff.samp animal 1110 R-structure: ~units post.mean l-95% CI u-95% CI eff.samp units 1110 Location effects: parity ~ log.med.depth post.mean l-95% CI u-95% CI eff.samp pMCMC (Intercept) 0.13854 -0.97336 1.4057652.98 0.87 log.med.depth -0.06105 -0.37972 0.3212214.31 0.69 # >summary(glm) Call: glm(formula = parity ~ log.med.depth, family = binomial(link = probit), data = traits) Deviance Residuals: Min 1Q Median 3Q Max -2.5976 -1.0564 0.5410 0.8522 1.6867 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 2.6195 0.2428 10.789 <2e-16 *** log.med.depth -0.9815 0.1030 -9.526 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 784.17 on 609 degrees of freedom Residual deviance: 683.16 on 608 degrees of freedom AIC: 687.16 Number of Fisher Scoring iterations: 4 Please let me know if there is any more info I can provide... Cheers, Chris On Thu, Dec 15, 2016 at 11:02 PM, Jarrod Hadfieldwrote: > Hi Chris, > > I think ngen in threshbayes is not the number of full iterations (i.e. a > full update of all parameters), but the number of full iterations > multiplied by the number of nodes (2n-1). With n=600 species this means > threshbayes has only really done about 8,000 iterations (i.e. about 1000X > less than MCMCglmm). Simulations suggest threshbayes is about half as > efficient per full iteration as MCMCglmm which means that it may have only > collected 0.5*1132/1200 = 0.47 effective samples from the posterior. The > very extreme value and the surprisingly tight credible intervals (+/-0.007) > also suggest a problem. > > **However**, the low effective sample size for the covariance in the > MCMglmm model is also worrying given the length of chain, and may point to > potential problems. Are egg-laying/live-bearing scattered throughout the > tree, or do they tend to aggregate a lot? Can you send me the output from: > > prior.dep<-=list(R=list(V=diag(1)*1e-15, fix=1), > G=list(G1=list(V=diag(1), fix=1))) > > dep<-MCMCglmm(parity~log.med.depth, >random=~animal, >rcov=~units, >pedigree=shark.tree, >reduced=TRUE, >data=traits, >prior=prior2, >pr=TRUE, >pl=TRUE, >family="threshold") > > summary(dep) > > summary(glm(parity~log.med.depth, data=traits, > family=binomial(link=probit))) > > Cheers, > > Jarrod > > > > On 15/12/2016 20:59, Chris Mull wrote: > > Hi All, > I am trying to look at the correlated evolution of traits using the > threshold model as implemented in phytools::threshBayes (Revell 2014) and > MCMCglmmRAM (Hadfield 2015). My understanding from Hadfield 2015 is that > the reduced animal models should yeild equivalent results, yet having run > both I am having trouble reconciling the results. I have a tree covering > ~600 species of sharks. skates, and rays and am interested in testing for > the correlated evolution between reproductive mode (egg-laying and > live-bearing) with depth. When I test for this correlation using > phytools:threshBayes there is a clear result with a high correlation > coefficient (-0.986) as I would predict. When I run the same analysis using > MCMCglmmRAM I get a very different result, with a low degree of covariation > and CI crossing zero (-0.374; -3.638 - 3.163 95%CI). Both models are run > for 10,000,000 generations with the same bunr-in and sampling period. I > have looked at the trace plots for each model using coda and parameter > estimates and likelihodd . I'm not sure how to reconcile the differences in > these results and any advice would be greatly appreciated. I have appended > the code and outputs below. > > > ### > #phytools::threshBayes# > ### > > X<-shark.data[c("parity","log.med.depth")] > X<-as.matrix(X) > > #mcmc paramters (also see control options) > ngen<-1000 > burnin<-0.2*ngen > sample<-500 > > thresh<-threshBayes(shark.tree, >X, >types=c("discrete","continuous"), >
Re: [R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi Chris, I think MCMCglmm is probably giving you the right answer. There are huge chunks of the phylogeny that are either egg-laying and live-bearing. The non-phylogenetic model shows a strong relationship between reproductive mode and depth, and that might be causal or it might just be because certain taxa tend to live at greater depths and *happen to have* the same reproductive mode. There's not much information in the phylogenetic spread of reproductive modes to distinguish between these hypotheses, hence the wide confidence intervals. Just to be sure can you a) just perform independent contrasts (not really suitable for binary data, but probably won't give you an answer far off the truth and is a nice simple sanity check). b) using MCMCglmm (not MCMCglmmRAM) fit prior.dep2<-=list(R=list(V=diag(1), fix=1), G=list(G1=list(V=diag(1), nu=0.002))) dep2<-MCMCglmm(parity~log.med.depth, random=~animal, rcov=~units, pedigree=shark.tree, data=traits, prior=prior.dep2, pr=TRUE, pl=TRUE, family="threshold") an send me the summary and hist(dep2$Liab) Cheers, Jarrod On 16/12/2016 07:02, Jarrod Hadfield wrote: Hi Chris, I think ngen in threshbayes is not the number of full iterations (i.e. a full update of all parameters), but the number of full iterations multiplied by the number of nodes (2n-1). With n=600 species this means threshbayes has only really done about 8,000 iterations (i.e. about 1000X less than MCMCglmm). Simulations suggest threshbayes is about half as efficient per full iteration as MCMCglmm which means that it may have only collected 0.5*1132/1200 = 0.47 effective samples from the posterior. The very extreme value and the surprisingly tight credible intervals (+/-0.007) also suggest a problem. *However*, the low effective sample size for the covariance in the MCMglmm model is also worrying given the length of chain, and may point to potential problems. Are egg-laying/live-bearing scattered throughout the tree, or do they tend to aggregate a lot? Can you send me the output from: prior.dep<-=list(R=list(V=diag(1)*1e-15, fix=1), G=list(G1=list(V=diag(1), fix=1))) dep<-MCMCglmm(parity~log.med.depth, random=~animal, rcov=~units, pedigree=shark.tree, reduced=TRUE, data=traits, prior=prior2, pr=TRUE, pl=TRUE, family="threshold") summary(dep) summary(glm(parity~log.med.depth, data=traits, family=binomial(link=probit))) Cheers, Jarrod On 15/12/2016 20:59, Chris Mull wrote: Hi All, I am trying to look at the correlated evolution of traits using the threshold model as implemented in phytools::threshBayes (Revell 2014) and MCMCglmmRAM (Hadfield 2015). My understanding from Hadfield 2015 is that the reduced animal models should yeild equivalent results, yet having run both I am having trouble reconciling the results. I have a tree covering ~600 species of sharks. skates, and rays and am interested in testing for the correlated evolution between reproductive mode (egg-laying and live-bearing) with depth. When I test for this correlation using phytools:threshBayes there is a clear result with a high correlation coefficient (-0.986) as I would predict. When I run the same analysis using MCMCglmmRAM I get a very different result, with a low degree of covariation and CI crossing zero (-0.374; -3.638 - 3.163 95%CI). Both models are run for 10,000,000 generations with the same bunr-in and sampling period. I have looked at the trace plots for each model using coda and parameter estimates and likelihodd . I'm not sure how to reconcile the differences in these results and any advice would be greatly appreciated. I have appended the code and outputs below. ### #phytools::threshBayes# ### X<-shark.data[c("parity","log.med.depth")] X<-as.matrix(X) #mcmc paramters (also see control options) ngen<-1000 burnin<-0.2*ngen sample<-500 thresh<-threshBayes(shark.tree, X, types=c("discrete","continuous"), ngen=ngen, control = list(sample=sample)) The return correlation is -0.986 (-0.99 - -0.976 95%HPD) # #MCMCglmm bivariate-gaussian# # prior2=list(R=list(V=diag(2)*1e-15, fix=1), G=list(G1=list(V=diag(2), nu=0.002, fix=2))) ellb.log.dep<-MCMCglmm(cbind(log.med.depth,parity)~trait-1, random=~us(trait):animal, rcov=~us(trait):units, pedigree=shark.tree, reduced=TRUE, data=traits,
Re: [R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi Chris, I think ngen in threshbayes is not the number of full iterations (i.e. a full update of all parameters), but the number of full iterations multiplied by the number of nodes (2n-1). With n=600 species this means threshbayes has only really done about 8,000 iterations (i.e. about 1000X less than MCMCglmm). Simulations suggest threshbayes is about half as efficient per full iteration as MCMCglmm which means that it may have only collected 0.5*1132/1200 = 0.47 effective samples from the posterior. The very extreme value and the surprisingly tight credible intervals (+/-0.007) also suggest a problem. *However*, the low effective sample size for the covariance in the MCMglmm model is also worrying given the length of chain, and may point to potential problems. Are egg-laying/live-bearing scattered throughout the tree, or do they tend to aggregate a lot? Can you send me the output from: prior.dep<-=list(R=list(V=diag(1)*1e-15, fix=1), G=list(G1=list(V=diag(1), fix=1))) dep<-MCMCglmm(parity~log.med.depth, random=~animal, rcov=~units, pedigree=shark.tree, reduced=TRUE, data=traits, prior=prior2, pr=TRUE, pl=TRUE, family="threshold") summary(dep) summary(glm(parity~log.med.depth, data=traits, family=binomial(link=probit))) Cheers, Jarrod On 15/12/2016 20:59, Chris Mull wrote: Hi All, I am trying to look at the correlated evolution of traits using the threshold model as implemented in phytools::threshBayes (Revell 2014) and MCMCglmmRAM (Hadfield 2015). My understanding from Hadfield 2015 is that the reduced animal models should yeild equivalent results, yet having run both I am having trouble reconciling the results. I have a tree covering ~600 species of sharks. skates, and rays and am interested in testing for the correlated evolution between reproductive mode (egg-laying and live-bearing) with depth. When I test for this correlation using phytools:threshBayes there is a clear result with a high correlation coefficient (-0.986) as I would predict. When I run the same analysis using MCMCglmmRAM I get a very different result, with a low degree of covariation and CI crossing zero (-0.374; -3.638 - 3.163 95%CI). Both models are run for 10,000,000 generations with the same bunr-in and sampling period. I have looked at the trace plots for each model using coda and parameter estimates and likelihodd . I'm not sure how to reconcile the differences in these results and any advice would be greatly appreciated. I have appended the code and outputs below. ### #phytools::threshBayes# ### X<-shark.data[c("parity","log.med.depth")] X<-as.matrix(X) #mcmc paramters (also see control options) ngen<-1000 burnin<-0.2*ngen sample<-500 thresh<-threshBayes(shark.tree, X, types=c("discrete","continuous"), ngen=ngen, control = list(sample=sample)) The return correlation is -0.986 (-0.99 - -0.976 95%HPD) # #MCMCglmm bivariate-gaussian# # prior2=list(R=list(V=diag(2)*1e-15, fix=1), G=list(G1=list(V=diag(2), nu=0.002, fix=2))) ellb.log.dep<-MCMCglmm(cbind(log.med.depth,parity)~trait-1, random=~us(trait):animal, rcov=~us(trait):units, pedigree=shark.tree, reduced=TRUE, data=traits, prior=prior2, pr=TRUE, pl=TRUE, family=c("gaussian", "threshold"), thin=500, burnin = 100, nitt = 1000) summary(ellb.log.dep) Iterations = 101:501 Thinning interval = 500 Sample size = 18000 DIC: 2930.751 G-structure: ~us(trait):animal post.mean l-95% CI u-95% CI eff.samp traitscale.depth:traitscale.depth.animal16.965 15.092 18.864 18000 traitparity:traitscale.depth.animal -0.374 -3.6383.163 1132 traitscale.depth:traitparity.animal -0.374 -3.6383.163 1132 traitparity:traitparity.animal 1.0001.0001.000 0 R-structure: ~us(trait):units post.mean l-95% CI u-95% CI eff.samp traitscale.depth:traitscale.depth.units16.965 15.092 18.86418000 traitparity:traitscale.depth.units -0.374 -3.6383.163 1132 traitscale.depth:traitparity.units -0.374 -3.6383.163 1132 traitparity:traitparity.units 1.0001.0001.0000 Location effects: cbind(scale.depth, parity) ~ trait - 1 post.mean l-95% CI u-95% CI eff.samp pMCMC
[R-sig-phylo] Threshold models using threshBayes vs MCMCglmmRAM
Hi All, I am trying to look at the correlated evolution of traits using the threshold model as implemented in phytools::threshBayes (Revell 2014) and MCMCglmmRAM (Hadfield 2015). My understanding from Hadfield 2015 is that the reduced animal models should yeild equivalent results, yet having run both I am having trouble reconciling the results. I have a tree covering ~600 species of sharks. skates, and rays and am interested in testing for the correlated evolution between reproductive mode (egg-laying and live-bearing) with depth. When I test for this correlation using phytools:threshBayes there is a clear result with a high correlation coefficient (-0.986) as I would predict. When I run the same analysis using MCMCglmmRAM I get a very different result, with a low degree of covariation and CI crossing zero (-0.374; -3.638 - 3.163 95%CI). Both models are run for 10,000,000 generations with the same bunr-in and sampling period. I have looked at the trace plots for each model using coda and parameter estimates and likelihodd . I'm not sure how to reconcile the differences in these results and any advice would be greatly appreciated. I have appended the code and outputs below. ### #phytools::threshBayes# ### >X<-shark.data[c("parity","log.med.depth")] >X<-as.matrix(X) > >#mcmc paramters (also see control options) >ngen<-1000 >burnin<-0.2*ngen >sample<-500 > >thresh<-threshBayes(shark.tree, >X, >types=c("discrete","continuous"), >ngen=ngen, >control = list(sample=sample)) The return correlation is -0.986 (-0.99 - -0.976 95%HPD) # #MCMCglmm bivariate-gaussian# # >prior2=list(R=list(V=diag(2)*1e-15, fix=1), G=list(G1=list(V=diag(2), nu=0.002, fix=2))) > >ellb.log.dep<-MCMCglmm(cbind(log.med.depth,parity)~trait-1, > random=~us(trait):animal, > rcov=~us(trait):units, > pedigree=shark.tree, > reduced=TRUE, > data=traits, > prior=prior2, > pr=TRUE, > pl=TRUE, > family=c("gaussian", "threshold"), > thin=500, > burnin = 100, > nitt = 1000) > >summary(ellb.log.dep) Iterations = 101:501 Thinning interval = 500 Sample size = 18000 DIC: 2930.751 G-structure: ~us(trait):animal post.mean l-95% CI u-95% CI eff.samp traitscale.depth:traitscale.depth.animal16.965 15.092 18.864 18000 traitparity:traitscale.depth.animal -0.374 -3.6383.163 1132 traitscale.depth:traitparity.animal -0.374 -3.6383.163 1132 traitparity:traitparity.animal 1.0001.0001.000 0 R-structure: ~us(trait):units post.mean l-95% CI u-95% CI eff.samp traitscale.depth:traitscale.depth.units16.965 15.092 18.86418000 traitparity:traitscale.depth.units -0.374 -3.6383.163 1132 traitscale.depth:traitparity.units -0.374 -3.6383.163 1132 traitparity:traitparity.units 1.0001.0001.0000 Location effects: cbind(scale.depth, parity) ~ trait - 1 post.mean l-95% CI u-95% CI eff.samp pMCMC traitscale.depth 0.12297 -3.63655 4.0200518000 0.949 traitparity -0.02212 -1.00727 0.9338717058 0.971 Thanks for any and all input. Cheers, Chris -- Christopher Mull PhD Candidate, Shark Biology and Evolutionary Neuroecology Dulvy Lab Simon Fraser University Burnaby,B.C. V5A 1S6 Canada (778) 782-3989 twitter: @mrsharkbrain e-mail:cm...@sfu.ca www.christophermull.weebly.com www.earth2ocean.org [[alternative HTML version deleted]] ___ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/